The invention relates generally to computerized modeling of integrated circuits and, in particular, to methods for distributing process variables by spatial interpolation for use in a circuit simulation tool.
Electronic design automation (EDA) tools, such as circuit simulation tools, are routinely used to model integrated circuits. Effective circuit simulation tools permit a circuit designer to simulate the behavior of a complex design, identify any problems, and make alterations and enhancements to the integrated circuit before arriving at a final design. Circuit simulation tools formulate and solve the nonlinear algebraic differential equations associated with an integrated circuit design, as is known in the art. Accurate simulation modeling of on-chip process variables, such as film thicknesses, is essential to accurately model high-performance circuit behavior, such as timing, power consumption, functionality, and design yield.
Various different conventional statistical spatial correlation methods for process variables are available for use in circuit simulation tools. In bounding box methods, a box is drawn around the objects that may be correlated and, based upon some metric of the box (e.g., a diagonal), a nominal level of spatial correlation is assumed. Unfortunately, bounding box methods represent an experience-based, heuristic approach. In exact methods, a principal component analysis (PCA) is executed to exactly identify the spatial correlation for each set of objects for which spatial correlation information is desired. Unfortunately, exact methods are a relatively expensive approach that is rarely implemented in practical tools.
Rectangular grid methods, which represent the prevalent approach for statistical spatial correlation, employ a fixed rectangular grid smaller than the spatial correlation distance. A single PCA is performed and applied to all sets of objects being considered, as a function of which grid cell they occupy. The rectangular grid approach assumes that the spatial correlation is constant within each grid, which allows the spatial correlation to be considered by defining the contents of each grid element to be a linear combination of the raw statistical data in the surrounding grids. Although conceptually similar to the rectangular grid approach, the hexagonal grid approach may be more computationally accurate given the higher packing density and lowered directional dependence of hexagonal grid cells in comparison with rectangular grid cells.
None of these conventional approaches is capable of continuously distributing the process variables across a chip, which denotes a significant deficiency. In rectangular and hexagonal grid approaches, discontinuities occur across grid boundaries. Devices bounded within each of the individual grid regions behave identically. However, devices bounded in adjacent grid regions behave differently regardless of the spacing between these devices, which leads to a mismatch in behavior. Generally, conventional approaches fail to maintain the local spatial correlation and, more often than not, are computationally inefficient.
Statistically-corrected spatial interpolation is an approach that does allow the continuous distribution of on-chip process variables and it is also computationally efficient. However, conventional statistically-corrected spatial interpolation relies on a uniform array of seed points distributed at the vertices of equilateral triangles. The problem with this approach is that the statistical correlation-versus-distance behavior of the process variable being modeled cannot change as a function of position on the chip. Also, the mean and standard deviations of the distributed process variable cannot change as a function of position on the chip. So, the method can only be used to model process variables that have a homogeneous global statistical correlation versus distance, standard deviation, and mean. Further, the approach is a numerical one which adds difficulty in the implementation of the method in conventional circuit simulation tools.
Consequently, improved methods are needed for distributing process variables for use in circuit simulation tools that overcome these and other deficiencies of conventional approaches of distributing process variables.